Abstract: To utilize the limited number of nurses effectively and improve the job satisfaction of nurses, the integrated nurse scheduling problem is studied considering workload balance. A mixed integer fractional programming model is first developed to design an integrated nursing staffing, scheduling, and assignment plan for minimizing the number of employed nurses under the balanced workload of nurses and the limited working time. An Accelerated Logic Benders exact decomposition algorithm is designed to solve this model. Specifically, based on the hierarchical characteristics of the developed model, the Benders algorithm framework is utilized to decompose the original problem into one master problem and multiple sub-problems, which effectively eliminates the nonlinearity. Two acceleration strategies called ESMP enhancement strategy and Accelerated Logic Benders cut strategy, are proposed to improve the solution efficiency. The experimental results show that considering the workload balance does not incur extra labor costs and makes the workload of nurses more balanced. The ESMP enhancement strategy and the Accelerated Logic Benders decomposition algorithm are feasible and effective. Finally, some important management implications of the workload balance strategy are provided for nursing institutions. To sum up, the proposed model and algorithm provide powerful decision-supporting tools for nursing institutions to make integrated nurse scheduling decisions, which can effectively reduce their employment cost and improve the job satisfaction of nurses.

Key words: nurse scheduling; workload balance; Benders decomposition algorithm; Logic Benders cut